Monday, 28 September 2015

45 years ago, Michael Jackson and his troupe of brothers
famously claimed that counting is easy peasy. But how easy is it really? (We’ll
leave aside the matter of the simplicity of A B C and do re mi for present
purposes!)

Counting and basic arithmetic operations are often viewed as
paradigmatic cases of ‘easy’ mental operations. It might seem that we are all
‘born’ with the innate ability for basic arithmetic, given that we all seem to
engage in the practice of counting effortlessly. However, as anyone who has
cared for very young children knows, teaching a child how to count is typically
a process requiring relentless training. The child may well know how to recite
the order of numbers (‘one, two, three…’), but from that to associating each of
them to specific quantities is a big step. Even when they start getting the
hang of it, they typically do well with small quantities (say, up to 3), but
things get mixed up when it comes to counting more items. For example, they
need to resist the urge to point at the same item more than once in the
counting process, something that is in no way straightforward!

The later Wittgenstein was acutely aware of how much
training is involved in mastering the practice of counting and basic arithmetic
operations. (Recall that he was a schoolteacher for many years in the 1920s!)
Indeed, counting and adding objects can be described as a specific and rather
peculiar language game which must be learned by training, and which raises all
kinds of philosophical questions pertaining to what it is exactly that we are
doing when we count things. Perhaps my favorite passage in the whole of the Remarks on the Foundations of Mathematics
is #37 in part I:

Monday, 7 September 2015

By Catarina Dutilh Novaes
(This post can be safely classified as an instance of shameless self-promotion, but here we go anyway...) Last week Stephen Read and I delivered the full manuscript of the forthcoming Cambridge Companion to Medieval Logic to Cambridge University Press. We still need to go through the whole production process (including indexing), but at this point it is safe to assume the volume will appear somewhere in 2016. We've been working on this volume for nearly 3 years, and so we are suitably thrilled to be nearing completion!

Many people asked me about the Table of Contents for the volume, and so I figured I might as well make it public -- now that we know there will not be any changes to chapters and/or contributors. Here it is: